tailieunhanh - composite 2012 Part 7

Tham khảo tài liệu 'composite 2012 part 7', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Simple Optical Methods for Measuring Optical Nonlinearities and Rotational Viscosity in Nematic Liquid Crystals 113 A0 r z 2b where .1 CX . 2 - ị- is the incident beam intensity Io is the on-axis intensity at focus I . . I . . I is the nonlinear absorbance of the medium i I ex I 1 11 I is the effective length of the sample and L is the sample thickness. By combining Eq. 2a and Eq. 2b we obtain the complex electric field at the exit surface of the sample - - 11 2 . . I r z expi-a Ll . r z v 7 7 1 1 J exp tA l q r z 3 E r z exp ÍA0 1 i I exp -a L 2 According to the aberration-free approximation of a Gaussian beam which requires the Gaussian beam profile be approximated as being parabolic by expanding the exponential in the intensity and retaining only the quadratic term the nonlinear phase shift Eq. 2b can be approximated as 4 W r z sJ ĩị where . 0 . 1 z2 and qx flIoLtff. It is noted that Eq. 4 is always valid whether I or not. By substituting Eq. 4 into Eq. 3 and employing the complex beam parameter formulation Kwak et al. 1999 we have finally obtain the closed aperture Z-scan transmittance of the far-field at the aperture plane including both of the effects of nonlinear absorption and nonlinear refraction as follows 5 where VI1 J is the on-axis nonlinear phase at focus and . If 2 vl .- is the ratio of the imaginary part to the real part of the complex nonlinearity and is inversely proportional to the figure of merit FOM defined as I t A1 . . Lenz et al. 2000 . The nonlinear absorptive and refractive contributions to the closed aperture Z-scan transmittance are coupled in terms of n or FOM. When the aperture is removed however the Z-scan is irrelevant to beam distortion caused by nonlinear refraction and is only a function of the nonlinear absorption as mentioned above. Hence the nonlinear absorption coefficient can readily be determined from the open aperture Z-scan transmittance. By spatially integrating Eq. 2a at z over all . ill- j without having to include